This paper introduces a novel blind frequency offset estimator for quadrature amplitude modulated (QAM) signals. Specifically, after a preliminary frequency compensation, the estimator is based on the <i>¿/2</i>-folded phase histogram of the received data. Then, the frequency offset estimate is taken as the frequency compensation value that minimizes the mean square error between the phase histogram measured on the received samples and the reference phase probability density function analytically calculated in the case of zero frequency offset. The ¿/2 -folded phase histogram of the received data is here called Constellation Phase Signature, since it definitively characterizes the phase distribution of signal samples belonging to a particular QAM constellation, and it has already been employed to develop a gain-control-free phase estimator that well performs both for square and cross constellations. Also the here described frequency offset estimator has the remarkable property to be gain-control-free and, thus, it can be fruitfully employed in frequency acquisition stages. The asymptotic performance of the estimator has been analytically evaluated and assessed by numerical simulations. Theoretical analysis and numerical results show that the novel frequency offset estimator outperforms state-of-the art estimators in a wide range of signal-to-noise ratio (SNR) values.